Agricultural Markets. Spring Lecture 24

Transcription

1 Agricultural Markets Spring 2014

2 Two Finance Concepts My claim: the two critical ideas of finance (what you learn in MBA program). 1. Time Value of Money. 2. Risk Aversion and Pooling.

3 Time Value of Money Dollar today is worth more than dollar tomorrow. Because preferences. Delay is sacrifice. Invest that dollar today and receive dollar and tomorrow receive dollar and return (interest).

4 Interest Rate and Discount Factor The interest rate is the price paid by the market to defer consumption. Preferences: Impatience: ρ. Higher ρ more impatient; greater prefer today consumption versus tomorrow. Can vary across individuals; willingness to save. Those with smaller ρ value consumption tomorrow higher. 1 Discount factor: 1+ρ. With ρ > 0, DF < 1.

5 Present Value PV is used to value assets that produce a income over a number of periods. You seek to maximize wealth: how much are you willing to pay for an asset Z which yields a stream of income Y t for T periods (years)? V Z = T t=0 Y t (1 + r) t

6 British Consol British Consol (Consolidated Annuity) with a coupon rate of i in perpetuity. What is its value? Coupon rate is the interest rate paid (annually, semi annually, quarterly, etc) on the par or face value of the bond. Face value is the amount paid should the bond be deemed. Of course, the value of the bond depends on the interest rate. Let s assume the coupon rate is 3% and the par value is $1,000. So the annual interest payment made forever is 0.03 $1, 000 = $30. Denote the interest payment as y. Let, the opportunity cost of funds be denoted as r and say r = 4%. Let the DF be denoted as θ.

7 Value of Consol At 3% Coupon Rate V c = y (1 + r) 0 + y (1 + r) 1 + y (1 + r) 2 + =yθ 0 + yθ 1 + yθ 2 + =y(1 + θ 1 + θ 2 + ) = y 1 ( θ ) ( ) 1 + r 1.04 = y = 30 = $780. r 0.04

8 Magazine Subscription Multiple year magazine subscription. How much does it save? 1. Buy a three year subscription for a one time cost of $ Subscribe annually (three one year subscriptions) at $20 per year.

9 Magazine Subscription 1. Cost of the 3 year subscription is $50. In today s money. 2. Finance on credit card (18%) on unpaid balance. Cost of the 3 one year subscription is: ( ) 2 = Lower cost option is to purchase one three year subscription.

10 Uncertainty Fact of Life: uncertainty. Deep Insight: Payoffs are not guaranteed. How to cope with and respond to uncertainty? (Nobel: Lars Peter Hansen 2013)

11 One Answer: Aggregate (Pool) Insurance companies: spread risk over [large] number of people. Obama Care needed at least 7m subscribers, with a nontrivial proportion of the young. Investment firms: hold a portfolio of stocks and bonds. 1. Return from stocks: dividend plus price appreciation. 2. Bonds: interest payment and change in valuation. Except for Consols, bonds have a maturity (set life). So as bond holder do not need to sell. As long as bonds do not default bonds offer lower risk than stocks. Investment strategy: share of portfolio in stocks (equities) declines with the age of investor.

12 Insurance Will discuss in depth in couple of weeks when we discuss Chapter 14.

13 Portfolio Example Have funds to invest. Can invest in stocks or bonds. Buy market weight stock fund (e.g., S&P 500), corporate Bond fund or municipal bond fund. The stock fund averages a return of µ e = 9% with a standard deviation of σ e = 12.0%. The bond fund averages a return of µ b = 4% with a standard deviation of σ b 2%. s represent the share of your portfolio in stocks. Let R e denote the return on stocks and B the return on bonds. The return on the portfolio R p is the share weighted returns of the stock and bond fund: R p = sr e + (1 s)b.

14 Expected Portfolio Return E [R p (s)] =E [sr e + (1 s)b] =se [R e ] + (1 s)e [B] =sµ e + (1 s)µ b

15 Dispersion of Portfolio Return See Appendix B for correlation. Var[R p (s)] =Var[sR e + (1 s)b] =s 2 Var(R e ) + (1 s) 2 Var(B) + 2s(1 s)cov(r e, B)

16 Covariance and Correlation Cov(X, Y ) Measure of association between random variables X, Y. Correlation ρ(x, y) is the scaled covariance. ρ(x, y) = Cov(X, Y ) σ x σ y. 1. Unrelated (independent) ρ = 0, 2. Perfect positive correlation(ρ = 1). ρ(x, x) = Perfect negative correlation (ρ = 1).

17 One Caveat on correlation If two random variables are independent ρ = 0. Reverse not true: ρ(x, Y ) = 0 X, Y independent. Measures association not causality. Many people die in hospitals. Hospitals kill people.

18 Portfolio If the returns to Stocks and Bonds are independent of one another reduced variance. Var(R p ) = s 2 Var(R e ) + (1 s) 2 Var(B) + 0 If s =.5 then E[R p ] = 0.08, σ Rp = If returns Stocks and Bonds are perfectly positive correlated, no reduction in dispersion (risk). If returns Stocks and Bonds are perfectly negative correlated, then portfolio has no risk, σ Rp = 0.

19 Chapter 11 Introduces key ideas in chapter 11 and provides examples. Chapters 12 (Land), Chapter 13 (Credit) are among longest chapters in DE, Chapter 15 (Insurance) not as long. Repeated application of ideas in chapter 11.

20 Forensic Studies Till now standard diet of perfect competition model. Model of perfect competition useful to highlight impact of imperfections Competitive Model is the benchmark. Example: cost of monopoly? Answer: misallocation of resources from competitive equilibrium.

21 Key Departures Importance of information (who knows what? [when do they know it?] Incentives. There are limits to contracts.[2em] These limitations in a environment of uncertainty.

22 Contagion and Market failure Ray: Imperfect markets are contagious: market failure in some sector can lead to problems in other sectors. (p. 408) Imperfect markets sometimes called missing markets. Used this terminology, in Chapter 9 as fertility a response to missing (asset) markets. Market imperfect is neither a necessary or sufficient condition for government intervention. Must also have some evidence that government intervention will not suffer from same problems that cause some markets to be missing. Informal institutions reactions to market imperfections due to legal informational or incentive restrictions.

23 Examples: Information Hidden action; moral hazard We observe output (q) not effort (e). q = g(e) + ɛ. To elicit the right amount of effort pay piece. Many jobs q also no observable. Pay on salary. Must find other incentives to elicit effort. Once covered by insurance, may not make the same effort to avoid accident. Translate insurance into more salient terms. Purchase insurance against low grade in (this) course. General setting: principal and agent.

24 Information Unobserved Type Basic idea: agents (people, firms, etc.) are heterogenous. Labor market: (a) people who live to work; versus (b) people who work to live. Credit market: some people will do all in their power to repay loan. Another subgroup, not so much. Health Insurance: different lifestyles. Risk preferences: risk averse, risk loving.

25 Incentives: To overcome limited information The moral hazard examples illustrate the need of incentives to elicit the proper amount of effort. One possible solution to imperfect monitoring of employee effort is to offer a high wage. If caught shirking (loafing, goldbricking) fired. Some times output low because of bad luck. Bad luck out of worker s control. (cheap talk example) Risk and absence of insurance creates an inefficiency. Problems can be difficult. Second Best

26 Enforcement: Limited Liability Limited liability: a borrower is poor and has no assets to use as collateral for a loan. Lender can be paid back if project succeeds. Lender paid nothing if lender fails. Lender bears downsize risk, not borrower. Implication: credit rationing. Borrower can not borrow as much as want at going market interest rate. Some (the poorest) may have no access to credit. Charging higher rate of interest will attract the more risky borrowers.

27 Enforcement: Breaking Agreements Insurance scheme in which several people in village put funds into pot to insure one another against fluctuations in output. If person A has a good harvest, and person B does not, then mutual insurance a will send money to B. How to enforce the contract between A and B? What sanctions can be used to force B to pay A? At a minimum A and B must be able to observe enough to detect another s misbehavior. How to enforce contract when courts do not exist or if they are incapable of verification.

28 Puzzling Questions Ray lists four puzzling questions of transactions which would not occur within perfect market setting: Why do landowners ask for a share of the tenant s crop instead of a fixed payment, which would save the landowners the cost of verifying and measuring output. Why might an indebted tenant not be forced to give up his land to a landlord to whom he might owe money? Why do some moneylenders advance loans at low, even zero rates of interest? Why are similar laborers given different contractual packages with different values?

29 Spillovers among Land, labor, capital, credit markets Several examples listed in Section 11.3 to highlight the role of informal institutions attempting to compensate for missing or imperfect market. Basic Idea: the more flexible markets will attempt to adjust for the failings of the less flexible markets, bringing the flexible inputs into line with the inflexible ones. For example, in situation of restricted credit, land and labor markets are both likely to funnel inputs in the direction of those who have access to capital equipment or bullocks.

30 Market Failure in Animal Power Animal power (bullocks) functions poorly if it functions at all (market failure). 1. Animals may be overworked. 2. Animals used in time bound activities: everyone needs to harvest crops at same time. To compensate market failure: the operational distribution of land may follow the ownership distribution of bullocks (i.e., land rented to farmers with bullocks). So owners of bullock may be able to lease land and hire labor.

31 Markets connected Easy to miss critical insight: land, labor, capital, credit, insurance markets are connected: to understand operation in one must consider some or all of the others. Imperfection (or nonexistence, e.g., insurance) in one spills over into the others. Consider setting where all five (land, labor, capital, credit, insurance) markets exist and function well. Then can consider (analyze) operation of one independently of the others. Agents need operate in only one market. Large land owner would hire labor, but with CRS would not also rent additional land.